Cyber-attack accommodation in a cyber-physical system is to ensure system operation, integrity and availability while maintaining a reasonable operational performance under attack. In this paper, we present a novel cyber-attack accommodation algorithm by estimating the true operational states of the system with new boundary & performance constrained resilient estimators while the system is continuously operating and is under attack. Our approach is based on combining data driven machine learning and physics based domain knowledge with traditional resilient estimation. The results were evaluated using a high fidelity model-based simulation environment.